Question

You wish to test the following claim (Ha) at a significance level of α=0.05.
      Ho:p1=p2
      Ha:p1>p2

You obtain a sample from the first population with 74 successes and 143 failures. You obtain a sample from the second population with 80 successes and 282 failures. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.

1. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = ______

2. What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = ______

3. The p-value is... ______

a) less than (or equal to) α

b) greater than α

4. This test statistic leads to a decision to... ______

a) reject the null

b) accept the null

c) fail to reject the null

5. As such, the final conclusion is that... _____

a) There is sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.

b) There is not sufficient evidence to warrant rejection of the claim that the first population proportion is greater than the second population proportion.

c) The sample data support the claim that the first population proportion is greater than the second population proportion.

d) There is not sufficient sample evidence to support the claim that the first population proportion is greater than the second population proportion.

Answer 1

significance level =  α=0.05.
      Ho:p1=p2
      Ha:p1>p2

x1 = 74 , n1 = 143 + 74 = 217

x2= 80 , n2 = 282 + 80 = 362

1. What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic = Z=((p1−p2)−0)/√(p(1−p)/(n1+n2)) = 3.16

test statistic = 3.16

2. What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value = P(z>3.16) = 0.0008

p-value = 0.0008

3. The p-value is... ______

a) less than (or equal to) α

4. This test statistic leads to a decision to... ______

a) reject the null

5. As such, the final conclusion is that... _____

c) The sample data support the claim that the first population proportion is greater than the second population proportion.